A Short Course in Computational Geometry and Topology

Herbert Edelsbrunner (Autor)

Buch | Softcover

IX, 110 Seiten

2014 | 2014
Springer International Publishing (Verlag)
978-3-319-05956-3 (ISBN)

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This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.

Roots of Geometry and Topology.- Voronoi and Delaunay Diagrams.- Weighted Diagrams.- Three Dimensions.- Alpha Complexes.- Holes.- Area Formulas.- Topological Spaces.- Homology Groups.- Complex Construction.- Filtrations.- PL Functions.- Matrix Reduction.- Epilogue.

Erscheint lt. Verlag	12.5.2014
Reihe/Serie	SpringerBriefs in Applied Sciences and Technology
Reihe/Serie	SpringerBriefs in Mathematical Methods
Zusatzinfo	IX, 110 p. 64 illus., 60 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	199 g
Themenwelt	Mathematik / Informatik ► Informatik
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Alpha Complexes • Computational Biology • Delaunay Triangulations • Persistent Homology • Protein Folding and Protein Docking • Simplicial Complexes • Voronoid Diagrams
ISBN-10	3-319-05956-4 / 3319059564
ISBN-13	978-3-319-05956-3 / 9783319059563
Zustand	Neuware